I would question note 2: “This assumes that it is possible to single out positive properties from among all properties. Gödel comments that “Positive means positive in the moral aesthetic sense (independently of the accidental structure of the world)…” – in other words, it’s man-made or anthropocentric.

Two probable limits are 1) Nothing may be infinitely dense, and 2) Nothing may be infinitely hot.

Okay, where (who?) guarantees those limits. Logic? In such a state, how can one be sure of logic without some sort of guarantor (God?). Logic isn’t even dependable on the quantum level. Quantum entanglement, for example.

Unseen hasn’t gone to the dark side. Rather, I thought it’d be interesting to imagine talking to a believer who isn’t simply dragging out centuries old, long refuted arguments first proposed in the Middle Ages or earlier like the watchmaker (design) argument, the ontological argument, the first cause argument, etc.

Of course, God needn’t be the only explanation for the way things are. Things may be the way they are, including the built-in mathematics, because this is the way things would be in this sort of universe. This universe would be a different sort of place, in other worlds, without the built-in math.

I always viewed math as an inherent property of the physical world and therefore does not present any special problem for disbelief in any of the “revealed” claims for the existence of deities. Special numbers such as Pi or e are to be expected. We have simply discovered math, it is not just a language (all though we have invented a symbolic language to pursue it). In fact, I would even say probability reigns supreme, the bell curve governs most outcomes and if anything this fact disproves the claim that prayers are answered.

I do not claim the existence of something “supernatural” that can exist outside of our universe (whatever that means, LOL) is impossible. How could we know? However, math and logic certainly are not valid arguments for any of the claimed gods and the so-called “logical proofs” of a some god are useless.

Our universe keeps on getting bigger. First, we thought there was nothing beyond our landmass other than perhaps dragons. Then, we learned there were elsewheres on other land masses. Then, we realized we were on a world and that it was round. The our universe keeps on getting bigger. Next, it was a solar system. Then a galaxy. Then a plethora of galaxies in a vast universe so big that we have no idea how big it really is. Then, we discover that the universe we know is just a small portion of what’s there (the “dark” part of our universe).

Now, it appears that there’s a super universe in which our universe, and probably others, exists.

ls there a super-duper universe in which the super universe exists, along with possibly others?

Math is a language used to describe the Universe we exist in. I recall hearing a mathematician say that for her PhD she mostly did her math using symbols and seldom used numbers except to work the symbols.

Math is a language used to describe the Universe we exist in. I recall hearing a mathematician say that for her PhD she mostly did her math using symbols and seldom used numbers except to work the symbols.

Math is part of the universe with or with people. We use a symbolic language to communicate ideas but the ratio we call Pi will still be here when we are gone and the volume of a sphere will still be 4/3 times P times R cubed. A constant ratio is a physical property.

Yes,the observations humans have made about the properties of the observable Universe would exist without us. Another evolved and sentient form of life on another planet would reach the same ideas about Pi, angles, fractals, circles etc. They too would use their own language of mathematics to describe the Universe as they see it and also understand those observations would still be true if they ceased to exist. If we met them on a neutral planet in another galaxy it would not take long for us to understand we both use the same math to get to that planet. We would have the same understanding of Reality. It is only when we get to the quantum or sub atomic level that we realize that “Reality” is not quite as it seems. I suppose it is time to mention the Anthropic Principle now?

If have to disagree. Math is completely separate from the laws of the universe. It’s a human construct, a human representation/modeling/conceptualisation/rendering/whatever-other-noun that we use to understand and survive in the hostile universe (and that math grows more complex as civilizations do). If humans were the only sentient beings in the history of the universe…then math did not exist until the first person made their first equation. And even then it was almost certainly counting the number of food items or animals around. He killed 2 birds, I killed 1 bird…therefore we have…uh….ummmmmmm…ehhhhhhh…three birds? The universe doesn’t count. Nor does it even distinguish objects. There is nowhere in the universe where you can find 1+1=2. Where is it? Does the solar system use π to determine the volume of a moon? Are there +s and -s and xs and ÷s hidden in black holes? Do planets do some arithmetic before deciding how far to orbit their star? Does the universe work out integrals when cosmic rays are spat out of supernovae? When the big bang happened…were compound fractions released? Is the universe limited to human number annotation? Can the laws of the universe suddenly shift in a way that makes math irrelevant/impossible?

The same goes for symbolic logic. Or critical thinking. The universe goes on quite find without humans doing logical arguments ∀x(P(x)→Q(x)).

The universe never used that, does it and you won’t find it anywhere where sentient life is absent. And to a much lesser extent (a very weak analogy) the same goes for musical notation, maps and calendars. While not the best comparison, its still the case that no maps could possibly exist without sentient (or even semi-sentient) beings.

When a bat echo locates in the dark with soundwaves, I’d say it is doing sophisticated math. It uses the speed of sound in it’s calculations and even factors in the doppler shift in it’s transmissions to determine distance to an object.

I see math in broader terms. It is semantics really, but the our sun is constantly calculating the speed of light. The universe is full of natural calculators doing the math of the universe all the time. Maybe it’s because I am an electrical engineer and rely on universal constants and relationships every day just to keep aircraft in the air, LOL.